In this paper an asymptotic expansion for the distribution of integrated periodograms w(λ) dλ is proved, where In (λ) denotes the periodogram of a stationary Gaussian random sequence and w(λ) is a weight function. This result is applied to obtain an expansion for the distribution of parameter estimates for the spectral density of the process.
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Wiltrud Mühleis (1984) studied this question.
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